Quaternionic Pole Placement via Companion Forms and the Ackermann Formula
We present an extension of state-feedback pole placement for quaternionic systems, based on companion forms and the Ackermann formula. For controllable single-input quaternionic LTI models, we define a companion polynomial that right-annihilates its companion matrix, characterize spectra via right-eigenvalue similarity classes, and prove coefficient-matching design in controllable coordinates. We then derive a coordinate-free Ackermann gain expression valid for real target polynomials, and stat…
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